The diagram shows five isosceles right angled prisms.A light ray incident at`90^(@)`at the first face emerge at same angle with the normal from the last face.Which of the following relations will hold regarding the refractive indices?

Options

A. `mu_(1)^(2) + mu_(3)^(2) + mu_(5)^(2) = mu_(2)^(2) + mu_(4)^(2)`
B. `mu_(1)^(2) + mu_(3)^(2) + mu_(5)^(2) = 1 + mu_(2)^(2) + mu_(4)^(2)`
C. `mu_(1)^(2) + mu_(3)^(2) + mu_(5)^(2) = 2 + mu_(2)^(2) + mu_(4)^(2)`
D. None of these

Answer

B

Explanation

`1 "sin" 90^(@) = mu_(1) "sin"r_(1)`,
`mu_(2) "sin"r_(2) = mu_(1)"cos"r_(1)`
`mu_(2)"cos"r_(2) = mu_(3)"sin"r_(3)`
`mu_(4) "sin"r_(4) = mu_(3)"cos"r_(3)`,
`mu_(4) "cos"r_(4) = mu_(5)"sin"r_(5)`
`1. "sin" 90^(@) = mu_(5) "cos"r_(5)`
Square and add `1 + mu_(2)^(2) + mu_(4)^(2) = mu_(1)^(2) + mu_(3)^(2) + mu_(5)^(2)`